MODELING DYNAMIC STALL OF SC-1095 AIRFOIL - SMARTech

123 Pages·2010·5.38 MB·English

by  Brian Clark

MODELING DYNAMIC STALL OF SC-1095 AIRFOIL AT
HIGH MACH NUMBERS

A Thesis
Presented To
The Academic Faculty

By

Brian Clark

In Partial Fulfillment
of the Requirements for the Degree
Master of Science in the
School of Aerospace Engineering

Georgia Institute of Technology

May 2010
MODELING DYNAMIC STALL OF SC-1095 AIRFOIL AT
HIGH MACH NUMBERS

Approved by:

Dr. Lakshmi Sankar
School of Aerospace Engineering
Georgia Institute of Technology

Dr. J.V.R. Prasad
School of Aerospace Engineering
Georgia Institute of Technology

Dr. Mark Costello
School of Aerospace Engineering
Georgia Institute of Technology

Date Approved: January 15, 2010
ACKNOWLEDGEMENTS

I would like to sincerely thank my advisor, Dr. Lakshmi Sankar. His
patience and advice were invaluable to the completion of this work. I also owe a
debt of gratitude to other graduate students working in the CFD lab that have
assisted me over the course of my studies at Georgia Tech. Nischint Rajmohan
and Jeremy Bain in particular have dedicated much of their time to assist me,
and their help is greatly appreciated. Finally, I would like to acknowledge the
emotional support and encouragement I have routinely received from friends and
family.

 ii
TABLE OF CONTENTS

ACKNOWLEDGEMENTS..........................................................................................................ii

LIST
OF
TABLES........................................................................................................................v

LIST
OF
FIGURES.....................................................................................................................vi

NOMENCLATURE.....................................................................................................................ix

SUMMARY................................................................................................................................xii

CHAPTER
1:
INTRODUCTION...............................................................................................1

CHAPTER
2:
RESEARCH
OBJECTIVES.................................................................................5

CHAPTER
3:
ANATOMY
OF
DYNAMIC
STALL...................................................................7

CHAPTER
4:
LEISHMAN­BEDDOES
MODEL...................................................................10

Attached Flow Model...................................................................................................................10

Separated Flow Model.................................................................................................................15

Dynamic Stall Model with Vortex Shedding.......................................................................20

Subsystem Interaction................................................................................................................23

CHAPTER
5:
VALIDATION
OF
THE
LEISHMAN­BEDDOES
MODEL.........................25

CHAPTER
6:
DESCRIPTION
AND
VALIDATION
OF
THE
CFD
TOOLS......................30

CHAPTER
7:
ASSESSMENT
OF
THE
LEISHMAN­BEDDOES
MODEL........................37

CHAPTER
8:
MODIFICATIONS
TO
THE
MODEL
AND
DISCUSSIONS.......................58

Lift Curve Slope and Zero Lift AoA........................................................................................58

Dynamic Stall Pitching Moment Vortex Convection Time Constant, T ................60

vl
Trailing Edge Separation Time Constant, T.......................................................................61

f

 iii
Effective Separation Point.........................................................................................................62

Center of Pressure........................................................................................................................66

Indicial Constants..........................................................................................................................72

Post Modification Results and Discussion.........................................................................75

CHAPTER
9:
CONCLUSIONS
AND
RECOMMENDATIONS...........................................88

APPENDIX
A:
DERIVATION
OF
LEISHMAN
BEDDOES
PARAMETERS....................90

REFERENCES.........................................................................................................................108



 iv
LIST OF TABLES

Table 1: Test Matrix.................................................................................................................................5

Table 2: Empirical Parameters Used in Leishman-Beddoes Method.........................24

Table 3: Modifications to Cna and Zero Lift AoA...................................................................58

Table 4: T Values................................................................................................................................61

vl
Table 5: Sensitivity of A1, A2, b1, and b2.................................................................................74

Table 6: Sensitivity of A3, A4, b3, and b4.................................................................................74

Table 7: Sensitivity of b5....................................................................................................................74



 v
LIST OF FIGURES

Figure 1: Comparison of CFD and NN Reduced Order Model (ROM)[26]....................4

Figure 2: The Effect of Dynamic Stall on NACA 0012 Airfoil[9]..........................................8

Figure 3: Forces Acting on Airfoil..................................................................................................10

Figure 4: Diagram Showing Flow Separation on an Airfoil...............................................16

Figure 5: Leishman-Beddoes Results, k=.075, α =9, α =8............................................26

m C
Figure 6: Leishman-Beddoes Results, k=.075, α =12, α =8.........................................27

m C
Figure 7: Leishman-Beddoes Results, k=.075, α =15, α =8.........................................28

m C
Figure 8: Drag Coefficient, M=0.4, k=.075, α =10.3, α =8.1.........................................29

m C
Figure 9: CFD Computational Grid...............................................................................................31

Figure 10: Close-up of Grid Around Airfoil................................................................................31

Figure 11: Predicted and Observed Airloads Using KES Model[24].............................32

Figure 12: Comparison of CFD Results and Exp Data, M=0.3, k=.03, α =15,
m
α =10..................................................................................................................................................33

C
Figure 13: Comparison of CFD Results and Exp Data, M=0.3, k=.05, α =15,
m
α =10..................................................................................................................................................34

C
Figure 14: Comparison of Experimental, CFD, and Leishman-Beddoes Results35

Figure 15: OVERFLOW Results Including Windtunnel Walls[28]...................................36

Figure 16: M=0.3, α =10, α =10, k=0.03..................................................................................38

m c
Figure 17: M=0.3, α =10, α =10, k=0.05..................................................................................39

m c
Figure 18: M=0.3, α =10, α =10, k=0.1.....................................................................................40

m c
Figure 19: M=0.3, α =5, α =5, k=0.05........................................................................................41

m c
Figure 20: M=0.4, α =10, α =10, k=0.03..................................................................................42

m c
Figure 21: M=0.4, α =10, α =10, k=0.05..................................................................................43

m c
Figure 22: M=0.4, α =10, α =10, k=0.1.....................................................................................44

m c
Figure 23: M=0.4, α =5, α =5, k=0.5..........................................................................................45

m c

 vi
Figure 24: M=0.5, α =7, α =4, k=0.03........................................................................................46

m c
Figure 25: M=0.5, α =7, α =4, k=0.05........................................................................................47

m c
Figure 26: M=0.5, α =7, α =4, k=0.1..........................................................................................48

m c
Figure 27: M=0.5, α =3, α =2, k=0.05........................................................................................49

m c
Figure 28: M=0.6, α =7, α =4, k=0.03........................................................................................50

m c
Figure 29: M=0.6, α =7, α =4, k=0.05........................................................................................51

m c
Figure 30: M=0.6, α =7, α =4, k=0.1..........................................................................................52

m c
Figure 31: M=0.6, α =3, α =2, k=0.05........................................................................................53

m c
Figure 32: M=0.7, α =5, α =2, k=0.03........................................................................................54

m c
Figure 33: M=0.7, α =5, α =2, k=0.05........................................................................................55

m c
Figure 34: M=0.7, α =5, α =2, k=0.1..........................................................................................56

m c
Figure 35: M=0.7, α =2, α =1, k=0.05........................................................................................57

m c
Figure 36: Lift Coefficient After Cna and α Modification..................................................60

0
Figure 37: Effective Separation Point, M=0.3.........................................................................62

Figure 38: Effective Separation Point, M=0.4.........................................................................63

Figure 39: Effective Separation Point, M=0.5.........................................................................63

Figure 40: Effective Separation Point, M=0.6.........................................................................64

Figure 41: Effective Separation Point, M=0.7.........................................................................64

Figure 42: Center of Pressure, M=0.3, m=2............................................................................67

Figure 43: Center of Pressure, M=0.3, m=1............................................................................68

Figure 44: Center of Pressure, M=0.3, m=0.5........................................................................68

Figure 45: Center of Pressure, M=0.3, m=4............................................................................69

Figure 46: Center of Pressure, M=0.4, m=2............................................................................70

Figure 47: Center of Pressure, M=0.5, m=2............................................................................70

Figure 48: Center of Pressure, M=0.6, m=2............................................................................71

Figure 49: Center of Pressure, M=0.7, m=2............................................................................71


 vii
Figure 50: Post Modification, M=0.3, α =10, α =10, k=0.1.............................................76

m c
Figure 51: Post Modification, M=0.4, α =10, α =10, k=0.1.............................................77

m c
Figure 52: Post Modification, M=0.5, α =7, α =4, k=0.1..................................................78

m c
Figure 53: Post Modification, M=0.6, α =7, α =4, k=0.1..................................................79

m c
Figure 54: Post Modification, M=0.7, α =5, α =2, k=0.1..................................................80

m c
Figure 55: Flow Development, M=0.3, α =10, α =10, k=0.1..........................................82

m c
Figure 56: Flow Development, M=0.7, α =5, α =2, k=0.03.............................................83

m c
Figure 57: Normal Force including Separation, Cnf, M=0.7, α =5, α =2, k=0.1..85

m c
Figure 58: Separation Point, f, M=0.7, α =5, α =2, k=0.1................................................85

m c
Figure 59: Center of Pressure, M=0.7, α =5, α =2, k=0.1...............................................86

m c
Figure 60: Lift, Moment, and Drag Data at M=0.3................................................................91

Figure 61: Lift, Moment, and Drag Data at M=0.4................................................................92

Figure 62: Lift, Moment, and Drag Data at M=0.5................................................................93

Figure 63: Lift, Moment, and Drag Data at M=0.6................................................................94

Figure 64: Lift, Moment, and Drag Data at M=0.7................................................................95

Figure 65: Normal force curve slope, M=0.3...........................................................................97

Figure 66: Effective Separation Point vs. Angle of Attack, M=0.3................................98

Figure 67: Derivation of S1 Parameter, M=0.3.......................................................................99

Figure 68: Derivation of S2 Parameter, M=0.3....................................................................100

Figure 69: Derivation of k , M=0.3.............................................................................................101

0
Figure 70: Derivation of k constant, M=0.3..........................................................................103

1
Figure 71: Derivation of k constant, M=0.3..........................................................................103

2
Figure 72: Derivation of C Coefficient, M=0.3..................................................................105

n1
Figure 73: Derivation of η Coefficient, M=0.3......................................................................106


 viii
NOMENCLATURE

A1 Leishman-Beddoes constant, 0.3
A2 Leishman-Beddoes constant, 0.7
A3 Leishman-Beddoes constant, 1.5
A4 Leishman-Beddoes constant, -0.5
A5 Leishman-Beddoes constant, 1.0
b1 Leishman-Beddoes constant, 0.14
b2 Leishman-Beddoes constant, 0.53
b3 Leishman-Beddoes constant, 0.25
b4 Leishman-Beddoes constant, 0.1
b5 Leishman-Beddoes constant, 0.5
c Airfoil chord length, ft
Cc Coefficient for circulatory component
X
Cai Coefficient for non-circulatory (impulsive) component due to pitch
X
€
Cqi Coefficient for non-circulatory (impulsive) component due to pitch rate
X
€
Chord force coefficient
C
C
€
C Drag force coefficient
d
€
C Skin friction drag coefficient
d0
€
Lift force coefficient
C
l
C Pitching moment coefficient about quarter-chord
m
€
C Zero-lift pitching moment
m0
€

 ix